Dependency of resolvable gravitational spatial resolution on space-borne observation techniques

The so-called Colombo-Nyquist (Colombo, The global mapping of gravity with two satellites, 1984) rule in satellite geodesy has been revisited. This rule predicts that for a gravimetric satellite flying in a (near-)polar circular repeat orbit, the maximum resolvable geopotential spherical harmonic degree (lmax) is equal to half the number of orbital revolutions (nr) the satellite completes in one repeat period. This rule has been tested for different observation types, including geoid values at sea level along the satellite ground track, orbit perturbations (radial,along-track, cross-track), low-low satellite-to-satellite tracking, and satellite gravity gradiometry observations (all three diagonal components). Results show that the Colombo–Nyquist must be reformulated. Simulations indicate that the maximum resolvable degree is in fact equal to knr + 1, where k can be equal to 1, 2, or even 3 depending on the combination of observation types. However, the original rule is correct to some extent, considering that the quality of recovered gravity field models is homogeneous as a function of geographical longitude as long as l max < nr/2